FF_DS_AZ_LOOP Dynamic Savings Loop Discrete Distribution

back to Fan's Intro Math for Econ, Matlab Examples, or Dynamic Asset Repositories
This is the example vignette for function: ff_ds_az_loop from the MEconTools Package. F(a,z) discrete probability mass function given policy function solution with discretized savings choices.

Test FF_DS_AZ_LOOP Defaults

Call the function with defaults. By default, shows the asset policy function summary. Model parameters can be changed by the mp_params.
%mp_params
mp_params = containers.Map('KeyType','char', 'ValueType','any');
mp_params('fl_crra') = 1.5;
mp_params('fl_beta') = 0.94;
% call function
ff_ds_az_loop(mp_params);
Elapsed time is 0.191238 seconds. ---------------------------------------- xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx CONTAINER NAME: mp_ffcmd ND Array (Matrix etc) xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx i idx ndim numel rowN colN sum mean std coefvari min max _ ___ ____ _____ ____ ____ ______ ______ ______ ________ ___ ___ ap 1 1 2 700 100 7 9855.1 14.079 14.408 1.0234 0 50 xxx TABLE:ap xxxxxxxxxxxxxxxxxx c1 c2 c3 c4 c5 c6 c7 ______ ______ ______ ________ _______ _______ ______ r1 0 0 0 0.045213 0.25576 0.61095 1.0362 r2 0 0 0 0.045213 0.25576 0.61095 1.0362 r3 0 0 0 0.045213 0.25576 0.61095 1.0362 r4 0 0 0 0.06647 0.25576 0.61095 1.0362 r5 0 0 0 0.06647 0.25576 0.61095 1.164 r96 43.924 43.924 43.924 43.924 43.924 45.102 45.102 r97 45.102 45.102 45.102 45.102 45.102 46.298 46.298 r98 46.298 46.298 46.298 46.298 46.298 47.513 47.513 r99 47.513 47.513 47.513 47.513 47.513 48.747 48.747 r100 48.747 48.747 48.747 48.747 48.747 50 50 FF_DS_AZ_LOOP finished. Distribution took = 0.14487 ---------------------------------------- xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx CONTAINER NAME: mp_ddcmd ND Array (Matrix etc) xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx i idx ndim numel rowN colN sum mean std coefvari min max _ ___ ____ _____ ____ ____ ___ _________ _________ ________ ________ ________ fa 1 1 2 100 100 1 1 0.01 0.016114 1.6114 0 0.121 faz 2 2 2 700 100 7 1 0.0014286 0.0035847 2.5093 0 0.052693 fz 3 3 2 7 7 1 1 0.14286 0.11742 0.82196 0.015625 0.3125 xxx TABLE:fa xxxxxxxxxxxxxxxxxx c1 __________ r1 0.121 r2 0.00034068 r3 0 r4 0.010458 r5 0.0048751 r96 1.1148e-21 r97 3.227e-22 r98 7.9165e-23 r99 1.4982e-23 r100 1.7037e-24 xxx TABLE:faz xxxxxxxxxxxxxxxxxx c1 c2 c3 c4 c5 c6 c7 __________ __________ __________ __________ __________ __________ __________ r1 0.0084023 0.03778 0.052693 0.018985 0.0029243 0.00020787 5.6301e-06 r2 0.00018105 0.0001207 3.3528e-05 4.9671e-06 4.1392e-07 1.8397e-08 3.4068e-10 r3 0 0 0 0 0 0 0 r4 0.00016518 0.002081 0.005593 0.0022334 0.00035834 2.6032e-05 7.146e-07 r5 0.00021881 0.00067299 0.0026761 0.0011123 0.00018127 1.3278e-05 3.6641e-07 r96 1.7183e-25 2.8942e-24 2.2565e-23 1.0675e-22 3.1764e-22 4.9586e-22 1.6895e-22 r97 3.2228e-26 6.111e-25 5.3384e-24 2.7969e-23 9.0055e-23 1.4769e-22 5.1004e-23 r98 4.5065e-27 1.0023e-25 1.0174e-24 6.0677e-24 2.15e-23 3.7371e-23 1.3103e-23 r99 3.8775e-28 1.0954e-26 1.38e-25 9.8022e-25 3.9213e-24 7.3193e-24 2.6118e-24 r100 1.1692e-29 5.3148e-28 9.7109e-27 8.9563e-26 4.2252e-25 8.6574e-25 3.1562e-25 xxx TABLE:fz xxxxxxxxxxxxxxxxxx c1 ________ r1 0.015625 r2 0.09375 r3 0.23438 r4 0.3125 r5 0.23438 r6 0.09375 r7 0.015625

Test FF_DS_AZ_LOOP Speed Tests

Call the function with different a and z grid size, print out speed:
mp_support = containers.Map('KeyType','char', 'ValueType','any');
mp_support('bl_timer') = true;
mp_support('ls_ffcmd') = {};
mp_support('ls_ddcmd') = {};
mp_support('ls_ddgrh') = {};
mp_support('bl_show_stats_table') = false;
% A grid 50, shock grid 5:
mp_params = containers.Map('KeyType','char', 'ValueType','any');
mp_params('it_a_n') = 50;
mp_params('it_z_n') = 5;
ff_ds_az_loop(mp_params, mp_support);
Elapsed time is 0.021787 seconds. FF_DS_AZ_LOOP finished. Distribution took = 0.046636
% A grid 100, shock grid 7:
mp_params = containers.Map('KeyType','char', 'ValueType','any');
mp_params('it_a_n') = 100;
mp_params('it_z_n') = 7;
ff_ds_az_loop(mp_params, mp_support);
Elapsed time is 0.218465 seconds. FF_DS_AZ_LOOP finished. Distribution took = 0.13608
% A grid 200, shock grid 9:
mp_params = containers.Map('KeyType','char', 'ValueType','any');
mp_params('it_a_n') = 200;
mp_params('it_z_n') = 9;
ff_ds_az_loop(mp_params, mp_support);
Elapsed time is 0.489370 seconds. FF_DS_AZ_LOOP finished. Distribution took = 0.35393

Test FF_DS_AZ_LOOP A grid 100 Shock grid 7

Call the function with different a and z grid size, print out speed:
mp_support = containers.Map('KeyType','char', 'ValueType','any');
mp_support('bl_timer') = true;
mp_support('ls_ffcmd') = {};
mp_support('ls_ddcmd') = {};
mp_support('ls_ddgrh') = {'faz','fa'};
mp_support('bl_show_stats_table') = true;
mp_params = containers.Map('KeyType','char', 'ValueType','any');
mp_params('it_a_n') = 100;
mp_params('it_z_n') = 7;
ff_ds_az_loop(mp_params, mp_support);
Elapsed time is 0.217312 seconds. FF_DS_AZ_LOOP finished. Distribution took = 0.1105
xxx tb_outcomes: all stats xxx OriginalVariableNames ap v c y coh savefraccoh ______________________ __________ __________ __________ __________ __________ ___________ {'mean' } 2.7094 6.6576 1.5089 1.5084 4.2183 0.48487 {'unweighted_sum' } 1439.4 7299.4 1545.9 1473.6 11549 479.94 {'sd' } 2.8976 2.0599 0.35843 0.52611 3.2096 0.25477 {'coefofvar' } 1.0694 0.3094 0.23755 0.34879 0.76088 0.52544 {'gini' } 0.53346 0.17414 0.13326 0.19097 0.39103 0.29771 {'min' } 0 1.6927 0.58543 0.58543 0.58543 0 {'max' } 50 19.139 4.9969 4.9969 54.997 0.93121 {'pYis0' } 0.070216 0 0 0 0 0.070216 {'pYls0' } 0 0 0 0 0 0 {'pYgr0' } 0.92978 1 1 1 1 0.92978 {'pYisMINY' } 0.070216 0.0057675 0.0057675 0.0057675 0.0057675 0.070216 {'pYisMAXY' } 2.1143e-10 3.7149e-11 3.7149e-11 3.7149e-11 3.7149e-11 2.065e-11 {'p0_01' } 0 1.6927 0.58543 0.58543 0.58543 0 {'p0_1' } 0 1.6927 0.58543 0.58543 0.58543 0 {'p1' } 0 2.7674 0.76855 0.61362 0.76855 0 {'p5' } 0 3.273 0.91608 0.77504 1.009 0 {'p10' } 0.06647 4.0961 1.0308 0.92803 1.1055 0.067651 {'p20' } 0.37601 4.8781 1.2371 1.0319 1.555 0.22796 {'p25' } 0.52503 5.2636 1.2781 1.0731 1.8354 0.28067 {'p30' } 0.7048 5.4822 1.3424 1.1472 2.0866 0.35907 {'p40' } 1.3008 6.0574 1.3953 1.3424 2.6774 0.48584 {'p50' } 1.9422 6.542 1.4931 1.4023 3.3444 0.54915 {'p60' } 2.5275 7.1265 1.6174 1.4954 4.1208 0.60499 {'p70' } 3.456 7.657 1.6502 1.7803 5.1554 0.67918 {'p75' } 3.9869 8.0469 1.733 1.824 5.7555 0.69673 {'p80' } 4.564 8.4125 1.8179 1.8875 6.1793 0.72076 {'p90' } 6.5844 9.3821 1.9734 2.3349 8.568 0.76882 {'p95' } 8.1844 10.225 2.1388 2.4776 10.358 0.80411 {'p99' } 13.136 11.834 2.3359 3.1677 15.511 0.85404 {'p99_9' } 18.839 13.486 2.7733 3.4782 21.332 0.88316 {'p99_99' } 21.778 14.354 3.0939 3.7505 24.78 0.89063 {'fl_cov_ap' } 8.396 5.2587 0.88866 0.93721 9.2847 0.58458 {'fl_cor_ap' } 1 0.88106 0.85565 0.61478 0.99833 0.7919 {'fl_cov_v' } 5.2587 4.243 0.71989 0.93806 5.9786 0.453 {'fl_cor_v' } 0.88106 1 0.97505 0.86559 0.90428 0.86321 {'fl_cov_c' } 0.88866 0.71989 0.12847 0.15253 1.0171 0.079518 {'fl_cor_c' } 0.85565 0.97505 1 0.80886 0.88413 0.8708 {'fl_cov_y' } 0.93721 0.93806 0.15253 0.2768 1.0897 0.080824 {'fl_cor_y' } 0.61478 0.86559 0.80886 1 0.64534 0.603 {'fl_cov_coh' } 9.2847 5.9786 1.0171 1.0897 10.302 0.6641 {'fl_cor_coh' } 0.99833 0.90428 0.88413 0.64534 1 0.81215 {'fl_cov_savefraccoh'} 0.58458 0.453 0.079518 0.080824 0.6641 0.064906 {'fl_cor_savefraccoh'} 0.7919 0.86321 0.8708 0.603 0.81215 1 {'fracByP0_01' } 0 0.0014664 0.0022377 0.0022385 0.00080043 0 {'fracByP0_1' } 0 0.0014664 0.0022377 0.0022385 0.00080043 0 {'fracByP1' } 0 0.0029302 0.01567 0.00403 0.0055106 0 {'fracByP5' } 0 0.021763 0.026172 0.02466 0.015702 0 {'fracByP10' } 0.0004071 0.050764 0.058937 0.05144 0.022123 0.0021411 {'fracByP20' } 0.0096198 0.1171 0.13549 0.11855 0.05416 0.033082 {'fracByP25' } 0.017608 0.15851 0.17677 0.15694 0.074837 0.057303 {'fracByP30' } 0.02761 0.19906 0.21973 0.19018 0.09783 0.092029 {'fracByP40' } 0.071719 0.28454 0.3135 0.28477 0.15542 0.18016 {'fracByP50' } 0.15388 0.38017 0.40577 0.38385 0.23227 0.28549 {'fracByP60' } 0.21684 0.48325 0.51534 0.46249 0.31381 0.4039 {'fracByP70' } 0.32573 0.59393 0.62048 0.57438 0.42716 0.54543 {'fracByP75' } 0.39815 0.65416 0.68002 0.63899 0.4882 0.60905 {'fracByP80' } 0.48482 0.72413 0.732 0.69931 0.55881 0.6822 {'fracByP90' } 0.6819 0.84902 0.85906 0.8281 0.73338 0.83355 {'fracByP95' } 0.79123 0.91664 0.92592 0.90812 0.83969 0.91574 {'fracByP99' } 0.9433 0.98136 0.98418 0.97889 0.95655 0.98225 {'fracByP99_9' } 0.99595 0.99805 0.99819 0.99776 0.99501 0.99858 {'fracByP99_99' } 0.99934 0.99982 0.99985 0.9998 0.99938 0.99984

Test FF_DS_AZ_LOOP A grid 300 Shock Grid 25

mp_support = containers.Map('KeyType','char', 'ValueType','any');
mp_support('bl_timer') = true;
mp_support('ls_ffcmd') = {};
mp_support('ls_ddcmd') = {};
mp_support('ls_ddgrh') = {'faz','fa'};
mp_support('bl_show_stats_table') = true;
mp_params = containers.Map('KeyType','char', 'ValueType','any');
mp_params('it_a_n') = 300;
mp_params('it_z_n') = 25;
ff_ds_az_loop(mp_params, mp_support);
Elapsed time is 1.356902 seconds. FF_DS_AZ_LOOP finished. Distribution took = 1.3706
xxx tb_outcomes: all stats xxx OriginalVariableNames ap v c y coh savefraccoh ______________________ __________ __________ __________ __________ __________ ___________ {'mean' } 3.1835 6.9106 1.5286 1.5274 4.7121 0.52236 {'unweighted_sum' } 4296.5 79518 16864 19751 1.2716e+05 5295.3 {'sd' } 3.2831 2.152 0.35175 0.53521 3.5973 0.25161 {'coefofvar' } 1.0313 0.31141 0.2301 0.35041 0.76341 0.48168 {'gini' } 0.52466 0.17565 0.12887 0.19155 0.39536 0.26998 {'min' } 0 -2.7621 0.25871 0.25871 0.25871 0 {'max' } 50 20.027 8.7798 8.7798 58.78 0.93152 {'pYis0' } 0.050267 0 0 0 0 0.050267 {'pYls0' } 0 7.4299e-05 0 0 0 0 {'pYgr0' } 0.94973 0.99993 1 1 1 0.94973 {'pYisMINY' } 0.050267 3.1587e-08 3.1587e-08 3.1587e-08 3.1587e-08 0.050267 {'pYisMAXY' } 2.3964e-09 9.6288e-14 9.6288e-14 9.6288e-14 9.6288e-14 2.6173e-22 {'p0_01' } 0 0.33524 0.44588 0.42089 0.44588 0 {'p0_1' } 0 1.0281 0.51088 0.51088 0.51088 0 {'p1' } 0 2.3294 0.67069 0.67069 0.67069 0 {'p5' } 0 3.531 0.9348 0.80006 1.0088 0 {'p10' } 0.10107 4.1808 1.0877 0.90775 1.2209 0.086874 {'p20' } 0.48982 5.0629 1.248 1.0638 1.7564 0.28154 {'p25' } 0.7256 5.3749 1.3048 1.157 2.0452 0.35473 {'p30' } 0.97897 5.7085 1.3561 1.192 2.3425 0.4186 {'p40' } 1.5756 6.2702 1.4389 1.3331 2.9951 0.51678 {'p50' } 2.2184 6.8025 1.5235 1.4352 3.7422 0.59639 {'p60' } 2.9972 7.3608 1.6237 1.5724 4.6044 0.65168 {'p70' } 4.012 7.977 1.7017 1.7487 5.6899 0.7051 {'p75' } 4.5871 8.3254 1.7349 1.8191 6.3522 0.72563 {'p80' } 5.3173 8.7116 1.8227 1.9222 7.1504 0.74857 {'p90' } 7.5009 9.7584 1.9829 2.2334 9.526 0.79537 {'p95' } 9.6743 10.633 2.1133 2.5088 11.809 0.82382 {'p99' } 14.854 12.286 2.3901 3.1545 17.176 0.86207 {'p99_9' } 21.166 14.023 2.7913 3.9726 23.779 0.88709 {'p99_99' } 26.803 15.357 3.0931 4.7968 29.914 0.89989 {'fl_cov_ap' } 10.779 6.2944 1.019 1.0643 11.798 0.64446 {'fl_cor_ap' } 1 0.89089 0.88234 0.60566 0.99894 0.78015 {'fl_cov_v' } 6.2944 4.6311 0.7528 0.97564 7.0472 0.46366 {'fl_cor_v' } 0.89089 1 0.9945 0.84708 0.91033 0.85631 {'fl_cov_c' } 1.019 0.7528 0.12373 0.15568 1.1427 0.077608 {'fl_cor_c' } 0.88234 0.9945 1 0.82696 0.90306 0.8769 {'fl_cov_y' } 1.0643 0.97564 0.15568 0.28645 1.2199 0.077311 {'fl_cor_y' } 0.60566 0.84708 0.82696 1 0.63363 0.57411 {'fl_cov_coh' } 11.798 7.0472 1.1427 1.2199 12.941 0.72207 {'fl_cor_coh' } 0.99894 0.91033 0.90306 0.63363 1 0.79776 {'fl_cov_savefraccoh'} 0.64446 0.46366 0.077608 0.077311 0.72207 0.063308 {'fl_cor_savefraccoh'} 0.78015 0.85631 0.8769 0.57411 0.79776 1 {'fracByP0_01' } 0 7.366e-06 9.1288e-05 2.5324e-05 2.9613e-05 0 {'fracByP0_1' } 0 0.00015226 0.00040756 0.00048297 0.00013202 0 {'fracByP1' } 0 0.0031657 0.0040997 0.0058265 0.0013172 0 {'fracByP5' } 0 0.020854 0.026015 0.023308 0.010613 0 {'fracByP10' } 0.0007829 0.049187 0.059665 0.051833 0.020313 0.0040897 {'fracByP20' } 0.010458 0.1169 0.13673 0.11782 0.052147 0.04121 {'fracByP25' } 0.020375 0.15489 0.17838 0.15407 0.072616 0.071271 {'fracByP30' } 0.033945 0.19501 0.22212 0.1924 0.09561 0.10878 {'fracByP40' } 0.076084 0.28102 0.3131 0.2752 0.15182 0.19951 {'fracByP50' } 0.13323 0.3766 0.41016 0.36618 0.22332 0.30599 {'fracByP60' } 0.21876 0.4783 0.51311 0.46472 0.31143 0.42495 {'fracByP70' } 0.32789 0.58936 0.62182 0.57246 0.4201 0.55532 {'fracByP75' } 0.39329 0.64823 0.67676 0.63063 0.48449 0.62358 {'fracByP80' } 0.47094 0.70976 0.73532 0.69204 0.55555 0.694 {'fracByP90' } 0.66575 0.84269 0.85851 0.82742 0.72907 0.84261 {'fracByP95' } 0.8001 0.91584 0.92543 0.90488 0.84038 0.91895 {'fracByP99' } 0.94734 0.98115 0.98337 0.97713 0.95746 0.98325 {'fracByP99_9' } 0.99324 0.99789 0.99809 0.99717 0.99445 0.9983 {'fracByP99_99' } 0.99909 0.99977 0.99979 0.99967 0.99931 0.99983

Test FF_DS_AZ_LOOP A grid 300 Shock Grid 50

mp_support = containers.Map('KeyType','char', 'ValueType','any');
mp_support('bl_timer') = true;
mp_support('ls_ffcmd') = {};
mp_support('ls_ddcmd') = {};
mp_support('ls_ddgrh') = {'faz','fa'};
mp_support('bl_show_stats_table') = true;
mp_params = containers.Map('KeyType','char', 'ValueType','any');
mp_params('it_a_n') = 300;
mp_params('it_z_n') = 50;
ff_ds_az_loop(mp_params, mp_support);
Elapsed time is 3.256673 seconds. FF_DS_AZ_LOOP finished. Distribution took = 3.3311
xxx tb_outcomes: all stats xxx OriginalVariableNames ap v c y coh savefraccoh ______________________ __________ __________ __________ __________ __________ ___________ {'mean' } 3.26 6.9484 1.5319 1.5305 4.7919 0.52772 {'unweighted_sum' } 4296.5 1.6217e+05 35821 53309 2.6813e+05 10814 {'sd' } 3.3166 2.1606 0.35167 0.5364 3.6315 0.25217 {'coefofvar' } 1.0174 0.31094 0.22956 0.35048 0.75783 0.47785 {'gini' } 0.52112 0.17551 0.12829 0.19134 0.39468 0.26727 {'min' } 0 -7.6871 0.12843 0.12843 0.12843 0 {'max' } 50 20.751 15.657 15.657 65.657 0.93164 {'pYis0' } 0.049546 0 0 0 0 0.049546 {'pYls0' } 0 0.00011924 0 0 0 0 {'pYgr0' } 0.95045 0.99988 1 1 1 0.95045 {'pYisMINY' } 0.049546 1.1021e-15 1.1021e-15 1.1021e-15 1.1021e-15 0.049546 {'pYisMAXY' } 5.1436e-09 3.0978e-19 3.0978e-19 3.0978e-19 3.0978e-19 7.4151e-23 {'p0_01' } 0 -0.20486 0.40271 0.40271 0.40271 0 {'p0_1' } 0 1.2135 0.53589 0.488 0.53589 0 {'p1' } 0 2.3687 0.71312 0.64833 0.71312 0 {'p5' } 0.00050419 3.5428 0.94895 0.8071 0.96945 0.00055062 {'p10' } 0.11149 4.2401 1.0944 0.93681 1.2484 0.095151 {'p20' } 0.51629 5.0791 1.255 1.072 1.7729 0.28687 {'p25' } 0.75904 5.4237 1.3033 1.1504 2.067 0.36257 {'p30' } 1.0189 5.7339 1.3518 1.2006 2.3841 0.42942 {'p40' } 1.6286 6.2919 1.446 1.3198 3.0593 0.53021 {'p50' } 2.2834 6.8389 1.5355 1.4423 3.8053 0.59978 {'p60' } 3.0751 7.4137 1.613 1.5765 4.7113 0.65858 {'p70' } 4.1046 8.0318 1.7011 1.7318 5.8286 0.70939 {'p75' } 4.7891 8.3723 1.7435 1.8266 6.5055 0.73443 {'p80' } 5.5379 8.765 1.8035 1.9295 7.3201 0.75699 {'p90' } 7.6355 9.7879 1.9921 2.2457 9.6214 0.79808 {'p95' } 9.8311 10.68 2.1096 2.5308 11.976 0.82663 {'p99' } 14.653 12.305 2.407 3.1554 17.087 0.86199 {'p99_9' } 21.166 14.067 2.7771 4.0255 23.953 0.88705 {'p99_99' } 27.382 15.467 3.1325 4.887 30.554 0.90105 {'fl_cov_ap' } 11 6.3988 1.032 1.0771 12.032 0.65387 {'fl_cor_ap' } 1 0.89298 0.88481 0.60546 0.99898 0.78182 {'fl_cov_v' } 6.3988 4.668 0.75538 0.97839 7.1542 0.46619 {'fl_cor_v' } 0.89298 1 0.99418 0.84423 0.91183 0.85567 {'fl_cov_c' } 1.032 0.75538 0.12367 0.15613 1.1557 0.077331 {'fl_cor_c' } 0.88481 0.99418 1 0.82768 0.90493 0.87203 {'fl_cov_y' } 1.0771 0.97839 0.15613 0.28772 1.2333 0.076912 {'fl_cor_y' } 0.60546 0.84423 0.82768 1 0.63312 0.56861 {'fl_cov_coh' } 12.032 7.1542 1.1557 1.2333 13.188 0.7312 {'fl_cor_coh' } 0.99898 0.91183 0.90493 0.63312 1 0.79848 {'fl_cov_savefraccoh'} 0.65387 0.46619 0.077331 0.076912 0.7312 0.063589 {'fl_cor_savefraccoh'} 0.78182 0.85567 0.87203 0.56861 0.79848 1 {'fracByP0_01' } 0 -7.082e-06 2.6291e-05 3.0744e-05 8.4044e-06 0 {'fracByP0_1' } 0 8.1705e-05 0.00058298 0.00029929 0.00018591 0 {'fracByP1' } 0 0.0025872 0.0055744 0.0043199 0.0017463 0 {'fracByP5' } 5.9482e-08 0.02063 0.028475 0.023256 0.0085179 3.9707e-07 {'fracByP10' } 0.00083251 0.049013 0.059787 0.051875 0.020182 0.004399 {'fracByP20' } 0.01069 0.11692 0.13707 0.11785 0.051473 0.041367 {'fracByP25' } 0.021006 0.15459 0.17869 0.15432 0.071586 0.072106 {'fracByP30' } 0.034297 0.19493 0.22235 0.19226 0.095063 0.10998 {'fracByP40' } 0.076942 0.2811 0.31433 0.27537 0.15173 0.20135 {'fracByP50' } 0.13547 0.37553 0.41049 0.36597 0.22294 0.30799 {'fracByP60' } 0.21688 0.47822 0.51321 0.46464 0.31179 0.42743 {'fracByP70' } 0.32617 0.58918 0.6213 0.57279 0.42106 0.55684 {'fracByP75' } 0.40001 0.64825 0.67795 0.6311 0.48455 0.62544 {'fracByP80' } 0.47816 0.71036 0.73507 0.69272 0.55654 0.69664 {'fracByP90' } 0.67319 0.84299 0.85862 0.82739 0.73089 0.84294 {'fracByP95' } 0.80347 0.91616 0.92515 0.90483 0.84244 0.91987 {'fracByP99' } 0.94675 0.98117 0.98325 0.97691 0.95831 0.98345 {'fracByP99_9' } 0.99284 0.99789 0.9981 0.99713 0.99445 0.99831 {'fracByP99_99' } 0.99909 0.99977 0.99979 0.99966 0.9993 0.99983